Step 1: Convert to Cartesian parametric form:
The line passes through $(0, -1, 3)$ with direction ratios $2, -2, 1$.
So any point on it has $x = 2\lambda$, $y = -1 - 2\lambda$ and $z = 3 + \lambda$.
Step 2: Add the three co-ordinates:
\[ x + y + z = 2\lambda - 1 - 2\lambda + 3 + \lambda = 2 + \lambda \]
The terms $2\lambda$ and $-2\lambda$ cancel, so only $\lambda$ stays.
Step 3: Set the sum equal to 3:
We need $2 + \lambda = 3$, so $\lambda = 1$.
Substitute back to get $x = 2$, $y = -3$, $z = 4$.
Step 4: Verify the point lies on the line:
The vector $(2, -3, 4) - (0, -1, 3) = (2, -2, 1)$, which is exactly the direction vector. So the point is on the line.
Final Answer:
The point is $(2, -3, 4)$. \[ \boxed{(2,\ -3,\ 4)} \]